How do I increase wave frequency of elastic fixed at one end?

Question

I am wanting to know all the ways to increase the frequency of waves in the elastic cord.

I know that I can decrease the mass of the trolley. I could also use stiffer springs (those with a larger spring constant).

Would any or all of these also work? A: use a shorter length of elastic B: move the single stand further from the trolley, to increase the tension C: move the two other stands in some way.

Or, would these things have no effect? I want to say they'd have no effect because it's a driven harmonic oscillator, but I can't construct an argument convincing enough to definitely rule them out.

Answer 1

The trolley provides a periodic driving force for waves in the elastic cord. This frequency is proportional to $\sqrt{k/m}$, so yes, increasing the stiffness of the spring and/or reducing the mass of the trolley will increase the driving frequency.

Doing something to the elastic cord will not affect the driving frequency (well, not much). Changing the length of the elastic cord will increase its tension $T$ and also reduce its mass per unit length $\mu$. These changes will affect the speed of waves on the cord $v=\sqrt{\frac{T}{\mu}}$. For a fixed driving frequency these changes will alter the wavelegth of waves on the cord.